a) Calculate the present values of each cash flow for a 3% three-year bond with annual coupons (the RRR is 4% in all years). Present the corresponding calculation for a 3% three-year bond with semi-annual coupons. Calculate the difference between the total PVs of these two bonds. Explain in a couple of sentences why this difference comes about.

b) Calculate how the total PV if the RRR rises from 4% to 4.01%(annual coupons is 3) Compare your PVs for these two different RRRs to derive an estimate of the duration of the bond. What is the reason for the difference between the maturity of this bond and its duration?

c) Now replace the 3% coupon bond with a three-year zero-coupon bond. Repeat your calculations from (b) for RRR equals 4% and 4.01% and hence derive an estimate for the duration of this zero-coupon bond. Explain why this duration is different to what you calculated for the coupon bond in (b).

d) Explain the difference between McCauley duration and modified duration. Which is a better measure of the risk that might result from shifts in the discount rate? Are your duration estimates above most comparable to the McCauley or the modified duration?